Abel-Prym Maps for Isotypical Components of Jacobians

摘要

Let C be a smooth non-rational projective curve over the complex field C. If A is an abelian subvariety of the Jacobian J (C), we consider theAbel-Prym map phi(A) : C -> A defined as the composition of the Abel map of C with the norm map of A. The goal of this work is to investigate the degree of the map phi(A) in the case where A is one of the components of an isotypical decomposition of J (C). In this case we obtain a lower bound for deg (phi(A)) and, under some hypotheses, also an upper bound. We then apply the results obtained to compute degrees of Abel-Prym maps in a few examples. In particular, these examples show that both bounds are sharp.